How to offset the texture coordinates of an object with an array modifier for mapping an image texture?
It needs a little tuning and tweaking with the y-location and y-scaling in the mapping node, but I think this would work:


Unwrap one board and make that board cover the complete image texture in the UV-image editor
Make an array with offset along the y-axis
Add a material to the mesh, with diffuse, image texture, mapping and texture coordinates (generated) as the image and tune and tweak the y-location and y-scaling in the mapping node.